In generating and constructing three-dimensional surfaces or bodies which have cross-sections that vary severely in shape along the surface to be constructed, it is particularly difficult to produce such surfaces with machine tools and machining operations, for example. Thus, if the surface to be constructed or reproduced possesses a particularly warped surface as present, for example, in propellers, three-dimensional cams, air foils, the machining of such surfaces with the application of machine tools involves labourious, tedious and therefore costly processes. Such surfaces are often produced with numerically controlled machine tools requiring controls in three-dimensions and corresponding instructions derived from computerized data based on complex calculations which must take into account the three-dimensional movement of the tool, together with the dimensions of the tool itself. Furthermore, machining of surfaces or bodies become particularly difficult if the surfaces to be constructed have substantially small cross-sectional areas, as, for example, if a hair is to be reproduced and fabricated. The machine tool, moreover, can often not reach recessed portions or cutouts in a surface or body.
Accordingly, it is an object of the present invention to provide an arrangement for generating and constructing three-dimensional surfaces and bodies in a simple and economical manner.
Another object of the present invention is to provide an arrangement of the foregoing character which is applicable to external as well as internal surfaces.
A further object of the present invention is to provide an arrangement, as described, in which the surfaces and bodies to be constructed have varying cross-sections and do not require axes of symmetry.